Improved Space-efficient Linear Time Algorithms for Some Classical Graph Problems

TL;DR

This paper presents improved space-efficient linear time algorithms for fundamental graph problems like bridges, topological sorting, and strongly connected components, enhancing previous methods with better space and input assumptions.

Contribution

The authors introduce new algorithms that are more space-efficient and operate in linear time for key graph problems, improving upon recent existing algorithms.

Findings

Algorithms for bridges, topological sorting, and SCCs run in linear time with reduced space.

New DFS implementation requires weaker input assumptions without losing efficiency.

Enhanced algorithms outperform previous methods in space and input requirements.

Abstract

This short note provides space-efficient linear time algorithms for computing bridges, topological sorting, and strongly connected components improving on several recent results of Elmasry et al. [STACS'15], Banerjee et al. [COCOON'16] and Chakraborty et al. [ISAAC'16]. En route, we also provide another DFS implementation with weaker input graph representation assumption without compromising on the time and space bounds of the earlier results of Banerjee et al. [COCOON'16] and Kammer et al. [MFCS'16].